IsGodAMathematician
From APIDesign
The philosphical parts of TheAPIBook were heavily influenced by The Key Stone of European Knowledge by Petr Vopěnka. I really mean inspired. The whole "key stone" book has more than 800 pages and thus TheAPIBook (of about 400) could cover just a tiny pieces. I'd like to recommend The Key Stone of European Knowledge to everyone as a reading is worth, but alas, the book is written in Czech and has not been translated to English.
This week I finished reading of "IsGodAMathematician?" and I think I can recommend it as a good enough substitute for the The Key Stone of European Knowledge. It has slightly different focus, it is shorter, yet it covers wider range of topics, yet I believe the way this book describes the beauty of Accient Greek's geometry matches the feel I've got when reading "the keystone" book.
Contents |
Flaws
I can only recommend reading IsGodAMathematician. I am especially glad that it references Galileo's thought experiement about speed of falling objects just like Chapter_1 of TheAPIBook. Reading this part was almost like reading my own explanation of the birth of Rationalism. Still I have few comments about differences between the work of Mario Livio and Petr Vopěnka.
Applied Math
At few moments I had a feeling that the description of the history of math is given from the point of view and its applications. Sure, that is expectable when the story is told by a physician, especially if one describes how it is possible math can describe real world. Moreover even the applied point of view is often more complex than what I understand (having master degree from a mathematical faculty - but from computer science department), because the math used these days by physicists is quite advanced.
Still one has to be aware of the limits. For example there is a single paragraph(!) in the whole book dedicated to computer science. One reference to computability theory only! The reach of the IsGodAMathematician is fairly large (thus not everything can be discussed in details), but given the fact that I spent four years at university discussing philosophical aspect of limitations of turing machines, I find omittion of this kind unfortunate. If the book was written for programmers, it would be a huge mistake.
Aristoteles
There is an interesting nuance discussed by Vopěnka in The Key Stone. Vopěnka patiently builds the reader's understanding that there is a significant difference between mathematics as envisioned by Platon and Aristoteles. There is nothing like that in [IsGodAMathematician]]. The whole mathematics inherited from Greeks threated as platonism and Aristoteles contribution is judged as minimal. This is probably acceptable from the physicist point of view, but Vopěnka has to (as a theoretical mathematists and an author of alternative set theory) seek for even the slightest differences. As even slight difference in the initial attitude may have magnificent consequences.
The Platon's geometrical world is given to us and we can just enlight more and more of it by focusing on already existing objects inside it (this is mentioned in IsGodAMathematician as wll). However, according to Vopěnka, Platon's math would be primarily based on evidences - on observing evident truths about the geometrical world. This is a kind of math that never had time to really become wide spread. Why? Because Aristoteles stepped in and gave us logic! Aristoteles changed the Platon's math dramatically by allowing us to use reason and logic (instead of direct evidence) to decide truths about geometrical objects.
The IsGodAMathematician has only small respect to Aristoteles mathematical skills and blames him for making many mistakes (btw. Vopěnka attributes important mistakes to Aristoteles geomatry as well). IsGodAMathematician would rather endorse Platon. But the truth is that the math as we know it (including those who prefer platonism) is significantly influenced by Aristoteles.
Understanding of God
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